Learning volatility-adaptive forgetting via GARCH-modulated LSTM for stock price forecasting

Xin-Rui Lu, Da-Qing Zhang

Stock price forecasting is hindered by the heteroscedastic nature of financial time series, in which turbulent and tranquil regimes alternate. Although the Long Short-Term Memory (LSTM) network is widely used for this task, its gates are oblivious to such volatility variation, so memory retention remains fixed regardless of market conditions. A common remedy is to supply volatility estimates as an additional input feature, yet this leaves the internal memory dynamics untouched. Instead, volatility can serve as a direct regulatory signal over the gate activation itself. This paper presents the Gsigmoid-LSTM model, which embeds Generalized Autoregressive Conditional Heteroscedasticity (GARCH(1,1))-derived volatility estimates into the LSTM forgetting gate through the Gsigmoid activation function, a volatility-adaptive variant of the sigmoid that combines a volatility adjustment factor with slope regulation via a learnable parameter. The model thereby automatically prioritizes recent information during turbulent periods while preserving long-term dependencies in stable markets. In the engineering application of daily stock price forecasting, extensive experiments, including…